Matching agents to objects using features in fast algorithm
Multi-Dimensional Matching
Computer Science and Game TheoryMachine LearningMultiagent Systems
Summary
Matching people or items usually requires knowing their full preferences, but this can be complicated. This paper studies a way to match agents and objects using just their features, which helps simplify the matching process. The authors use a mathematical method called spectral projection to turn this complex problem into an easier one-dimensional sorting task. Their approach guarantees good outcomes in terms of fairness and overall satisfaction but is not completely safe from people trying to game the system. They tested their method on an AI shopping example and with many random cases to confirm its behavior.
What this means in practice
- •For ai shopping platform developers: Use feature-based matching to efficiently recommend products aligning with buyer preferences while balancing fairness and overall satisfaction.$Commercial implications: Enables creation of AI shopping recommendation tools that optimize customer satisfaction and fairness through fast feature-based matching.
- •For marketplace platform engineers: Implement scalable agent-object matching in online markets where full preference rankings are not available but feature data exists.
Authors
Irene Aldridge
Abstract
We study a matching mechanism where agents and objects are described by features rather than complete rankings. A single spectral projection reduces the problem to a one-dimensional sort, computable in O(N log N) time. We prove that on descaled features and preferences, our algorithm obtains the exact Nash Social Welfare (NSW) optimum within the projected space, with an unconditional utilitarian-welfare guarantee and a conditional NSW guarantee. The proposed mechanism is stable against exogenous noise but not strategy-proof; we provide an explicit profitable misreport. On an agentic AI shopping application, the diagnostics correctly anticipate both a success and a failure case. A 100-instance robustness study confirms the findings.